A new sampling point scheme with nine evaluation points were introduced in this research study for twenty noded brick elements. The new sampling points were located inside the brick element at the corners and center point of the 20 node brick element. This integration scheme can be assumed to be an imitation of Gaussian integration scheme. Standard benchmark problems were chosen from the different research works and compared with our proposed scheme. Finally, the proposed integration scheme achieves good results for twenty node brick element on different performance parameters of finite element analysis.
An element edge method is developed for the evaluation of stiffness matrix for the 8-node brick element. Handling of large data leads to take more computational time in finite element analysis. The new set of quadrature consist of 13 sampling points and weights out which 12 points are at the edges of the brick element and one point is considered at the center of the element. The new set of sampling points is a mimic of Gauss numerical integration method. Finally, the proposed element edge method is evaluated using the standard benchmarked problems and compared the results with conventional Gauss integration method and found that CPU execution time for the evaluation of finite element problems are found to be reduced considerably without compromising in the results mainly consist of accuracy of values and convergence rate.
A new sampling point scheme with 13 evaluation points was introduced in this research study for 20-node brick elements. The new sampling points were located inside the brick element at the edges and the center point of the 20-node brick element. This integration scheme can be assumed to be an imitation of the Gaussian integration scheme. Standard benchmark problems were chosen from the different research works and compared with our proposed scheme. Finally, the proposed integration scheme achieves good results for 20-node brick elements on different performance parameters of finite element analysis.
Recently, many literature studies have focused on the development on new elements in finite elements. This paper aims to develop a new quadrature for the 3-node triangular element for the purpose of evaluation of element stiffness matrix. The analysis of triangular element is usually done in a quadrilateral element by dividing the quadrilateral element into two. The edge sampling point quadrature is a mimics of Gauss numerical integration scheme. This sampling integration scheme consists of five sampling points and weights where four sampling points are at the edge and one at the center of the element. Accuracy of results, convergence of the results and stability of values have been tested using the standard benchmarked problems defined by various research studies.
This research paper focuses on the objective of developing a quadrature for evaluating the element stiffness matrix for the four-node quadrilateral element in finite element analysis (FEA). The proposed integration scheme is defined as an element edge method (EEM), which mimics the Gauss numerical integration scheme. This integration scheme consists of five sampling points and weights where four integration point locations are at the edges and one is at the center of the quadrilateral element. The proposed quadrature scheme has been tested using various benchmarked problems designed by various researchers to study the convergence of the results, accuracy of results, and stability of values.
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